chore: adopt strict Ultracite and Effect linting

[ueberBrot]

Summary

Adopt Ultracite core, React, TanStack, Vitest and anti-slop presets plus Effect strict. Refactor the Scheduler, Management Surface, Management Adapters, Dashboard and tests to satisfy them, preserving public synchronous and Promise contracts. Keep compatibility exceptions scoped to existing public error contracts and supported test APIs.

 CI
- default lint → builds → separate type checks and typed lint
+ fast lint → builds → combined typed lint/typecheck → Astro check

Restore fmt:fix and fmt:check, declare Shoehorn in its five consuming workspaces, and declare Zod in docs. Includes cleanup of obsolete docs evidence images.

Evidence

• Before: Applying the initial strict presets exposed 5,663 lint errors and 440 warnings.
  After: The final configuration reports zero diagnostics across 407 files and 738 rules. Fast lint, Effect lint, formatting and Astro checks also pass.
• Tests: 1,622 tests across 127 files pass with none pending; all 420 Playwright E2E tests pass across desktop/mobile and authenticated variants.
• Packages: All six package builds, publint and attw pass; Dashboard development and docs builds pass.
• Public API: Exported declaration comparison against main reports zero differences. Packed-consumer scenarios minimum-core, minimum-management and current pass.

Merge Danger

Door: two-way

Revert the commit to restore the previous implementation and tooling.

Blast Radius: workspace

Broad refactors touch Scheduler behavior, Management Adapters and Dashboard. Passing runtime and consumer checks support compatibility; declaration equality verifies the exported type contracts.

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Latest commit: 3155cae

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